I really liked this. I enjoyed having so many different gods and creatures to encounter, as well as the description and imagery of the underworld itself. I’m curious what endings there will be – right now the MC is still trying to find Leonidas, but the longer she stays the more entangled she becomes, and I could see good and bad endings happening because of that.
Typos
The underworld is dangerous for one whose heart still beats, and you will find it full of denizens which at times may be benevolent, but more often hostile to your cause.
It looks like “which” should be “who” since it reads like you’re describing the denizens as benevolent. Add “are” before “hostile” as well if that’s the case.
You can still recall how his green eyes sparkled with mirth, while he ran his fingers through his short dark hair.
I’m not sure there needs to be a comma here.
You clutch the lyre given to you by your father Apollo tightly, its perfect sounds ringing out through the agora as you sing once more of your lost Leonidas.
This part was confusing at first because there’s no transition from being in the field on the day of the wedding to being at the agora in the present.
“Why must you continue to address me as such after all these years? That may have been the name you gave me, but none call me any longer except you.”
Add “that” after “call me”.
You flop into one of the couches, while your guest paces the tiled floor. Apollo combs fingers through his long golden hair, while his blue eyes are clouded with concern.
I don’t think either of these sentence should have commas either, although you might want to reword one to avoid the repititon of using “while” in the same paragraph.
“But none who are living may enter the realm of the dead. Besides, I don’t even know where the path to the Palace of Hades lies,” you reply despondently
Add a period at the end.
Servants have left food and water ready for your arrival before no doubt scared from the building by the presence your father.
Perhaps you should mention the food, water, and coins when Apollo first brings the MC into the room so there’s more description to the setting and don’t seem to appear out of nowhere.
Forge on, enduring wound made by the savage plants. You don’t want to risk damage to your lyre. You’ll likely need it again before this journey is over.
Add “the” after “enduring”.
“Show yourself”
Add a period or exclamation mark at the end.
“Cowards, to stalking from the shadows. Show yourself or be gone!” you demand.
Should “stalking” be “stalk”?
"I’m looking for someone called Leonidas.
Add a quotation mark at the end.
The presence in your mind stirs sluggishly before quieting once again almost as if being in this house has had a sedative effect on it. Ask Hecate what she knows of it."
Remove the quotation mark.
I see the God of Light and I rarely speak; especially these days given I spend most of my time down here beyond his reach.
Is the “I see” part supposed to part of this sentence?
Contracts: None. |You bargained with Hypnos for your release. In return, you promised to prepare a scrifice of herbs and flowers sacred to the god of sleep.|
In the stats screen – “scrifice” should be “sacrifice”.
Stats
Name: Myrrine, daughter of Apollo.
Location: Hecate’s Crossroads.
Frame of Mind: Heroic.
Vitality: Healthy.
Quest: In search of your lost love Leonidas, dead before his time.
Hunger: Hungry.
Thirst: Very dehydrated.
Contracts: None. |You bargained with Hypnos for your release. In return, you promised to prepare a scrifice of herbs and flowers sacred to the god of sleep.|
Items Carried: |Your precious lyre, gifted to you by Apollo.| |A purse full of coins.| |An enchanted silver necklace.|
Visited the night realm and encountered the oneoiri.
Locations undiscovered: 9, 10, 11, 13, 14
Looking forward to the next chapter and possibly meeting Persephone. 
) and kind of ended up making a very, very abbreviated version of this WIP.